On the finiteness of certain Rabinowitsch polynomials II Original Research Article

Let m be a positive integer and fm(x) be a polynomial of the form fm(x)=x2+x−m. We call a polynomial fm(x) a Rabinowitsch polynomial if for image and consecutive integers x=x0, x0+1,…,x0+t−1, f(x) is either 1 or prime. In Byeon (J. Number Theory 94 (2002) 177), we showed that there are only finitely many Rabinowitsch polynomials fm(x) such that 1+4m is square free. In this note, we shall remove the condition that 1+4m is square free.